Why Do We Test Multiple Traits in Genetic Association Studies?

Abstract

In studies of complex disorders such as nicotine dependence, it is common that researchers assess multiple variables related to a disorder as well as other disorders that are potentially correlated with the primary disorder of interest. In this work, we refer to those variables and disorders broadly as multiple traits. The multiple traits may or may not have a common causal genetic variant. Intuitively, it may be more powerful to accommodate multiple traits in genetic traits, but the analysis of multiple traits is generally more complicated than the analysis of a single trait. Furthermore, it is not well documented as to how much power we may potentially gain by considering multiple traits. Our aim is to enhance our understanding on this important and practical issue. We considered a variety of correlation structures between traits and the disease locus. To focus on the effect of accommodating multiple traits, we examined genetic models that are relatively simple so that we can pinpoint the factors affecting the power. We conducted simulation studies to explore the performance of testing multiple traits simultaneously and the performance of testing a single trait at a time in family-based association studies. Our simulation results demonstrated that the performance of testing multiple traits simultaneously is better than that of testing each trait individually for almost models considered. We also found that the power of association tests varies among the underlying models. The advantage of conducting a multiple traits test is minimized when some traits are influenced by the gene only through other traits; and it is maximized when there are causal relations between the traits and the gene, and among the traits themselves or when there are extraneous traits.

Figure 1

Forty causal structures among one disease gene G and three traits Y₁, Y₂ and Y₃ that are illustrated by DAGs. The arrows from G to Y_j and from Y_k to Y_j represent that there exist direct effects of G on Y_j and Y_k on Y_j for j, k = 1, 2, 3. The locations of Y₁, Y₂ and Y₃ can be exchanged arbitrarily in each structure.

Figure 2

Power of the two testing methods based on structures S7–S40 for quantitative traits. The black dots and the black triangles respectively represent the performance of single-trait test and multiple-trait test in absence of any extraneous variables, and the gray dots and the gray triangles respectively represent the performance of single-trait test and multiple-trait test in presence of extraneous variables, which result in positive correlations among traits. The nominal significance level is 0.01.

Figure 3

Power of the two testing methods based on structures S7–S40 for quantitative traits. The black dots and the black triangles respectively represent the performance of single-trait test and multiple-trait test in absence of any extraneous variables, and the gray dots and the gray triangles respectively represent the performance of single-trait test and multiple-trait test in presence of extraneous variables, which result in negative correlations among traits. The nominal significance level is 0.01.

Figure 4

Power of the two testing methods based on structures S7–S40 for binary traits. The black dots and the black triangles respectively represent the performance of singletrait test and multiple-trait test in absence of any extraneous variables, and the gray dots and the gray triangles respectively represent the performance of single-trait test and multiple-trait test in presence of extraneous variables, which result in positive correlations among traits. The nominal significance level is 0.01.

Figure 5

Power of the two testing methods based on structures S7–S40 for binary traits. The black dots and the black triangles respectively represent the performance of singletrait test and multiple-trait test in absence of any extraneous variables, and the gray dots and the gray triangles respectively represent the performance of single-trait test and multiple-trait test in presence of extraneous variables, which result in negative correlations among traits. The nominal significance level is 0.01.